Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+6)^3=25*(x+6)
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Equation 1-5x=-6x+8
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Equation 1-5*x=-6*x+8
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Equation x^2-8*x+17=0
- Express {x} in terms of y where:
- -7*x-7*y=-14
- 10*x-2*y=0
- -15*x+17*y=13
- -11*x-15*y=14
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Identical expressions
- six *cos(x)^(two)+ seven *cos(x)- three = zero
- 6 multiply by co sinus of e of (x) to the power of (2) plus 7 multiply by co sinus of e of (x) minus 3 equally 0
- six multiply by co sinus of e of (x) to the power of (two) plus seven multiply by co sinus of e of (x) minus three equally zero
- 6*cos(x)(2)+7*cos(x)-3=0
- 6*cosx2+7*cosx-3=0
- 6cos(x)^(2)+7cos(x)-3=0
- 6cos(x)(2)+7cos(x)-3=0
- 6cosx2+7cosx-3=0
- 6cosx^2+7cosx-3=0
- 6*cos(x)^(2)+7*cos(x)-3=O
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Similar expressions
- 6*cos(x)^(2)+7*cos(x)+3=0
- 6*cos(x)^(2)-7*cos(x)-3=0
- 6*cosx^(2)+7*cosx-3=0
6*cos(x)^(2)+7*cos(x)-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 6*cos (x) + 7*cos(x) - 3 = 0
$$6 \cos^{2}{\left(x \right)} + 7 \cos{\left(x \right)} - 3 = 0$$
Rapid solution
[src]
x_1 = -acos(1/3) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi$$
x_2 = acos(1/3)
$$x_{2} = \operatorname{acos}{\left(\frac{1}{3} \right)}$$
x_3 = -re(acos(-3/2)) + 2*pi - I*im(acos(-3/2))
$$x_{3} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}$$
x_4 = I*im(acos(-3/2)) + re(acos(-3/2))
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}$$
Sum and product of roots
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sum
-acos(1/3) + 2*pi + acos(1/3) + -re(acos(-3/2)) + 2*pi - I*im(acos(-3/2)) + I*im(acos(-3/2)) + re(acos(-3/2))
$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) + \left(\operatorname{acos}{\left(\frac{1}{3} \right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right)$$
=
4*pi
$$4 \pi$$
product
-acos(1/3) + 2*pi * acos(1/3) * -re(acos(-3/2)) + 2*pi - I*im(acos(-3/2)) * I*im(acos(-3/2)) + re(acos(-3/2))
$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) * \left(\operatorname{acos}{\left(\frac{1}{3} \right)}\right) * \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right) * \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right)$$
=
-(-acos(1/3) + 2*pi)*(I*im(acos(-3/2)) + re(acos(-3/2)))*(-2*pi + I*im(acos(-3/2)) + re(acos(-3/2)))*acos(1/3)
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right) \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{3}{2} \right)}\right)}\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Numerical answer
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x1 = -38.9300712604183
x2 = 13.7973300316999
x3 = -7.51414472452036
x4 = 76.6291831034958
x5 = 82.9123684106754
x6 = -20.0805153388795
x7 = -80.4504495759938
x8 = 20.0805153388795
x9 = 26.3637006460591
x10 = 42.7513377329163
x11 = -26.3637006460591
x12 = -1.23095941734077
x13 = 55.3177083472755
x14 = -11.3354111970184
x15 = 7.51414472452036
x16 = -57.7796271819571
x17 = 1458.929950683
x18 = 80.4504495759938
x19 = -64.0628124891366
x20 = 30.1849671185572
x21 = 38.9300712604183
x22 = -55.3177083472755
x23 = 23.9017818113776
x24 = 36.4681524257367
x25 = -89.195553717855
x26 = 11.3354111970184
x27 = -67.8840789616347
x28 = -1657.52996167807
x29 = 86.7336348831734
x30 = -51.4964418747775
x31 = 111.866376111892
x32 = -74.1672642688143
x33 = -49.0345230400959
x34 = -61.6008936544551
x35 = 74.1672642688143
x36 = -70.3459977963162
x37 = -93.016820190353
x38 = 32.6468859532387
x39 = 99.3000054975326
x40 = -99.3000054975326
x41 = 975.124682030177
x42 = 67.8840789616347
x43 = -95.4787390250346
x44 = -13.7973300316999
x45 = 70.3459977963162
x46 = 51.4964418747775
x47 = -36.4681524257367
x48 = 89.195553717855
x49 = 5.05222588983881
x50 = 61.6008936544551
x51 = -23.9017818113776
x52 = 17.618596504198
x53 = -76.6291831034958
x54 = -45.2132565675979
x55 = -5.05222588983881
x56 = 57.7796271819571
x57 = -30.1849671185572
x58 = 95.4787390250346
x59 = -32.6468859532387
x60 = -17.618596504198
x61 = 64.0628124891366
x61 = 64.0628124891366
The graph